相关论文: Lattice based extended formulations for integer li…
For a set $X$ of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with $X$ is called the relaxation complexity $\mathrm{rc}(X)$. This parameter was introduced by Kaibel &…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a…
The treated matrix equation $(1+ae^{-\frac{\|X\|}{b}})X=Y$ in this short note has its origin in a modelling approach to describe the nonlinear time-dependent mechanical behaviour of rubber. We classify the solvability of…
We give an optimal upper bound for the maximum-norm distance from a vertex of a knapsack polyhedron to its nearest feasible lattice point. In a randomised setting, we show that the upper bound can be significantly improved on average. As a…
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static…
For a linear matrix function $f$ in $X \in \R^{m\times n}$ we consider inhomogeneous linear matrix equations $f(X) = E$ for $E \neq 0$ that have or do not have solutions. For such systems we compute optimal norm constrained solutions…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which order a^2 errors are removed is presented. Order a^2 improvement of the gauge fixing condition displays the secondary…
In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer…
Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…
A new finite lattice calculation of the low lying bound state energies in the massive Schwinger model is presented, using a Hamiltonian lattice formulation. The results are compared with recent analytic series calculations in the low mass…
We present an application of the standard Langevin dynamics to the problem of weak coupling perturbative expansions for Lattice QCD. This method can be applied to the computation of the most general observables. In this preliminary work we…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We study the Lattice Isomorphism Problem (LIP), in which given two lattices L_1 and L_2 the goal is to decide whether there exists an orthogonal linear transformation mapping L_1 to L_2. Our main result is an algorithm for this problem…
Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that…
In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness.…